How To Add Complex Numbers

Video Tutorial on Adding Complex Numbers

Example 1 Let's add the following 2 complex numbers

(5 + 2i ) + (7 + 12i)

Step 1) Group the real part of the complex number and the imaginary part of the complex number.	(5 + 7) + (2i + 12i)
Step 2) Combine the like terms and simplify	12 + 14i

Problem 1) Add the following complex numbers:

(5 + 3i) + ( 2 + 7i)

Answer

This problem is very similar to example 1 .

Step 1) Group the real part of the complex number and the imaginary part of the complex number.	(5 + 2) + (3i + 7i)
Step 2) Combine the like terms and simplify	7 + 10i

Problem 2) Add the following 2 complex numbers

(9 + 11i) + (3 + 5i)

Answer

This problem is very similar to example 1 .

Step 1) Group the real part of the complex number and the imaginary part of the complex number.	(9 + 3) + (11i + 5i)
Step 2) Combine the like terms and simplify	12 + 16i

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Problem 3) Add the complex numbers below

(12 + 14i) + (3 -2i)

Answer

This problem is very similar to example 1 with the added twist that we have a negative number in there (-2i).

Step 1) Group the real part of the complex number and the imaginary part of the complex number.	(12 + 3) + (14i + -2i)
Step 2) Combine the like terms and simplify	15 + 12i

Problem 4) Add the following 2 complex numbers

(6 - 13i) + (12 + 8i)

Answer

This problem is very similar to example 1with the added twist that we have a negative number in there (-13i).

Step 1) Group the real part of the complex number and the imaginary part of the complex number.	(6 + 12) + (-13i + 8i)
Step 2) Combine the like terms and simplify	18 + 5i

Problem 4) Add the following complex numbers

(-2 - 15i) + (-12 + 13i)

Answer

Step 1) Group the real part of the complex number and the imaginary part of the complex number.	(-2 + -12) + (-15i + 13i)
Step 2) Combine the like terms and simplify	-14 + 2i